AI Startups Transforming Mathematics: The Race to Revolutionize Learning and Innovation

Today, mathematicians are in high demand by the world’s elite, as leading tech companies like OpenAI and Google are targeting top talent. Emerging startups are also joining the fray, riding the wave of recognition that mathematics is essential for enhancing artificial intelligence, potentially reshaping the field itself.

Ken Ono, a distinguished mathematician, expressed, “Last May, I felt my scientific identity fading.” He took a leave from his professorship at the University of Virginia in 2025 to join Axiom Math, a startup devoted to advancing AI with a focus on mathematics. He initially collaborated with Epoch AI to craft challenging math problems that test AI capabilities. “We quickly realized that these AI systems far exceeded our expectations. It felt akin to farmers encountering combustion engines and envisioning their vast potential,” added Ono.

This phenomenon is echoed by many in the industry. Axiom Math is one of several startups launched recently aimed at developing AI that not only performs mathematical tasks but also verifies its correctness. During my visit to various companies in Silicon Valley, I sought to understand their faith in mathematics as a cornerstone for an AI-driven future.

Axiom Math operates in Palo Alto, just a short distance from Stanford University, where founder Karina Hong, a former student of Ono, studied. Nearby, Harmonic, another startup, is striving for “mathematical superintelligence” that promises similarly verifiable outcomes. Despite their unassuming offices, these companies attract substantial investment, indicating strong belief in their potential.

In a modest office named after renowned mathematicians like Carl Friedrich Gauss and Ada Lovelace, I asked Ono about the need for startups like Axiom Math amidst larger entities like OpenAI and Google. He responded, “ChatGPT functions like a librarian—you can’t find what hasn’t been read. But do you want a librarian performing brain surgery?” Despite the success of language models like ChatGPT, their accuracy remains questionable without human validation, thus presenting a clear opportunity for a verification-focused approach.

Mathematical verification systems have been developed over the years, with the most notable being Lean, which allows mathematicians to translate proofs for quick computer verification—a helpful tool for research-level mathematics requiring extensive proof validation.

Verification in Complexity

Similar challenges arise in software development where language models generate large volumes of code often riddled with elusive bugs, requiring human oversight. Axiom Math and Harmonic are poised to tackle this as a revenue stream, especially where funding is scarce for complex mathematical inquiries. Just as Lean enables proof verification, software can also undergo mathematical validation, ensuring correctness and eliminating bugs. “As AI increasingly writes code, the demand for verification rises, as human oversight becomes a bottleneck,” stated Harmonic CEO, Tudor Achim.

While software verification is a primary revenue focus, both companies excel in AI that solves mathematical problems across various research fields, generating verified proofs in algebraic geometry and number theory. Axiom Math has seen five papers featuring AI-generated proofs accepted into mathematical journals. Although a specific roadmap for future challenges was not disclosed, Ono indicated plans to produce dozens of papers next year, shortening timelines from years to mere days.

These startups face intense competition as tech giants intensify their focus on AI-driven mathematical solutions. “Mathematics is a powerful tool for AI development due to its measurable nature,” remarked OpenAI lead scientist, Jakub Pachocchi. Early language models struggled with quantifiable content but have greatly improved since then.

Once perceived as inferior in basic mathematics, modern AI has achieved extraordinary milestones, including winning its first gold medal at the International Mathematics Olympiad, a contest once deemed beyond AI’s reach. Recently, it also disproved an 80-year-old mathematical conjecture, something thought impossible within a single lifetime by many mathematicians.

Sebastian Bubeck from OpenAI noted, “The limitations we observed six months ago were glaring. There were areas where models produced nonsensical outcomes. Today, that’s no longer an issue.” Unlike Axiom Math and Harmonic, which employ mathematicians to refine AI models, Bubeck stated that OpenAI focuses on creating intelligent systems broadly, rather than specifically optimizing for mathematics alone. “We are training for general AI, and this holistic enhancement will yield capabilities that could revolutionize mathematics,” he asserted.

Regardless of the winning strategy, mathematicians express concern that the domain of mathematics may dwindle into the hands of a few financially robust tech firms. This sudden surge in interest raises fears that it may vanish just as quickly. Rabbi Bakir from Stanford University expressed, “There’s significant investment now, and we’ll deeply feel its absence when it fades. While AI models can elevate mathematical reasoning, this advantage may not persist in five years, especially for groundbreaking problems like the Riemann hypothesis.”

The Paywall Dilemma

We may enter an era where access to mathematics becomes restricted, with solutions only available to those who can afford the necessary funding or exclusive AI models. Although Axiom Math currently offers many tools free of charge, there’s a looming possibility of future costs.

Shubo Sengupta, involved in axiomatic mathematics, remarked, “Some aspects of modern mathematics are already walled off. [Large hedge funds] engage in highly proprietary mathematical modeling inaccessible to others.” Sengupta advocates for unrestricted access to expand the boundaries of mathematical knowledge.

Achim from Harmonic shares a similar sentiment, “While tools aiding mathematicians come at a price, we aim to provide value for services. This doesn’t undermine our support for mathematicians; if a company believes in mathematics’s future significance, they should afford support to its practitioners.”

Predicting the future remains inherently challenging, especially with AI’s rapid advancements, yet mathematicians are expected to maintain a prominent role in shaping this landscape. Ono analogized the rise of AI-integrated mathematical systems to the emergence of Srinivasa Ramanujan, a self-taught mathematics prodigy whose unexpected insights revolutionized early 20th-century math.

Recalling his father’s inspiration stemming from Ramanujan, Ono shared, “Perhaps this is a transformative moment like Ramanujan’s. When we observe computers unveiling remarkable insights, we should embrace this reality, as it’s unfolding around us.”